Cardinal Invariants and Eventually Different Functions |
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Authors: | Hyttinen Tapani |
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Institution: | Department of Mathematics and Statistics, University of Helsinki P.O. Box 68, 00014, Finland; tapani.hyttinen{at}helsinki.fi |
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Abstract: | In this paper we study several kinds of maximal almost disjointfamilies. In the main result of this paper we show that forsuccessor cardinals , there is an unexpected connection betweeninvariants ae(), b() and a certain cardinal invariant md(+)on +. As a corollary we get for example the following result.For a successor cardinal , even assuming that < = and 2= +, the following is not provable in ZermeloFraenkelset theory. There is a +-cc poset which does not collapse andwhich forces a() = + < ae() = ++ = 2. We also apply the ideasfrom the proofs of these results to study a = a() and non(M).2000 Mathematics Subject Classification 03E17 (primary), 03E05(secondary). |
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